Since the model proposed by Frank (Frank FC, Biochem Biophys Acta 1953;11:459-463), several alternative models have been developed to explain how an asymmetric non-racemic steady state can be reached by a chirally symmetric chemical reactive system. This paper explains how a stable non-racemic regime can be obtained as a symmetry breaking occurring in a far-from-equilibrium reactive system initiated with an initial imbalance. Departing from the variations around the original Frank's model that are commonly described in the literature, i.e. open-flow systems of direct autocatalytic reactions, we discuss recent developments emphasizing both an active recycling of components and an autocatalytic network of simple reactions. We will present our APED model as the most natural realization of such thermodynamic openness and non-equilibrium, of recycling and of network autocatalysis, each of these in prebiotic conditions. The different experimental and theoretical models in the literature will be classified according to mechanism. The place and role of such self-structured networks responsible for the presence of homochirality in the primitive Earth will be detailed.